Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Scaling01:26

Scaling

557
In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
557
Calibration Curves: Linear Least Squares01:20

Calibration Curves: Linear Least Squares

4.1K
A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
For data that follow a straight line, the standard method for fitting is the linear...
4.1K
Curve Sketching and Derivatives01:22

Curve Sketching and Derivatives

8
Understanding the behavior of a function through its first and second derivatives is essential for analyzing its graph. Derivatives provide insight into where a function increases or decreases, where it attains local maxima or minima, and how its curvature behaves across different intervals.The first derivative of a function reveals the slope of the tangent line at any given point. Points where the derivative is zero or undefined are considered critical, as they often indicate potential extrema...
8
Modeling and Similitude01:12

Modeling and Similitude

613
Scaled modeling is a fundamental technique in engineering, enabling the study of large and complex systems by creating smaller, manageable replicas that recreate critical characteristics of the original. In hydrology and civil infrastructure, for example, scaled models of dams help analyze water flow, turbulence, and pressure. This method allows for accurate predictions of real-world behavior within a controlled environment, significantly reducing the cost and time involved in full-scale...
613
Guidelines for Sketching a Curve01:23

Guidelines for Sketching a Curve

12
Curve sketching is a systematic method for understanding the overall behavior of a function by analyzing its key mathematical features. A function defines a curve on the coordinate plane, where the horizontal axis represents the input variable and the vertical axis represents the output. The process begins by determining the domain, which specifies the set of input values for which the function is defined and establishes the horizontal extent of the graph.Intercepts with the horizontal and...
12
Properties of Fourier series II01:21

Properties of Fourier series II

532
Time scaling of signals is a crucial concept in signal processing that affects the Fourier series representation without altering its coefficients. The process modifies the fundamental frequency, thereby changing how the series represents the signal over time. This principle is essential in various applications, including audio and image processing, where signal manipulation is frequent. Understanding function symmetries is fundamental to simplifying the Fourier series.
A function f(t) is...
532

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Variable Resolution Maps (VRM) in CCTBX and Phenix: Accounting For Local Resolution In cryoEM.

bioRxiv : the preprint server for biology·2026
Same author

Explicit correction of severely non-uniform distributions of cryo-EM views.

Acta crystallographica. Section D, Structural biology·2026
Same author

Direct calculation of variable-resolution maps by fully analytic approximations to atomic images.

Journal of applied crystallography·2026
Same author

Quantifying distributions of cryo-EM projections.

Acta crystallographica. Section D, Structural biology·2026
Same author

Program <i>VUE</i>: analysing distributions of cryo-EM projections using uniform spherical grids.

Journal of applied crystallography·2024
Same author

Accounting for nonuniformity of bulk-solvent: A mosaic model.

Protein science : a publication of the Protein Society·2024

Related Experiment Video

Updated: Jan 15, 2026

Quantifying Fibrillar Collagen Organization with Curvelet Transform-Based Tools
07:58

Quantifying Fibrillar Collagen Organization with Curvelet Transform-Based Tools

Published on: November 11, 2020

6.7K

Rescaling FSC curves.

Alexandre G Urzhumtsev1

  • 1Centre for Integrative Biology, IGBMC (Institute of Genetics and of Molecular and Cellular Biology), CNRS-INSERM-University of Strasbourg, 67404 Illkirch, France.

Acta Crystallographica. Section D, Structural Biology
|October 8, 2025
PubMed
Summary

Comparing periodic functions in cryo-electron microscopy (cryoEM) can be biased by traditional resolution shell definitions. A new method using inverse cubic resolution scales creates balanced shells, improving statistical comparisons and potentially making Fourier shell correlation (FSC) analysis more robust.

Keywords:
FSC curveshalf-mapsinverse cubic resolutionpiecewise linear approximationresolution shellsuniformly filled shells

More Related Videos

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

3.0K
Routine Collection of High-Resolution cryo-EM Datasets Using 200 KV Transmission Electron Microscope
09:49

Routine Collection of High-Resolution cryo-EM Datasets Using 200 KV Transmission Electron Microscope

Published on: March 16, 2022

5.9K

Related Experiment Videos

Last Updated: Jan 15, 2026

Quantifying Fibrillar Collagen Organization with Curvelet Transform-Based Tools
07:58

Quantifying Fibrillar Collagen Organization with Curvelet Transform-Based Tools

Published on: November 11, 2020

6.7K
ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

3.0K
Routine Collection of High-Resolution cryo-EM Datasets Using 200 KV Transmission Electron Microscope
09:49

Routine Collection of High-Resolution cryo-EM Datasets Using 200 KV Transmission Electron Microscope

Published on: March 16, 2022

5.9K

Area of Science:

  • Structural biology
  • Biophysics
  • Computational science

Background:

  • Comparing periodic functions, common in crystallography and cryo-electron microscopy (cryoEM), typically involves analyzing Fourier coefficients within resolution shells.
  • Current cryoEM practices define shell boundaries uniformly in inverse resolution, leading to uneven distribution of coefficients and potentially biased statistical comparisons or misleading plots.

Purpose of the Study:

  • To address the imbalance in Fourier coefficients per resolution shell in cryo-electron microscopy (cryoEM).
  • To propose and evaluate a novel method for defining resolution shells that improves statistical comparisons and data visualization.

Main Methods:

  • Implementing a transformation to define resolution shell boundaries uniformly on the inverse cubic resolution scale.
  • Analyzing the distribution of Fourier coefficients across shells generated by the new method.
  • Evaluating the impact of the new shell definition on Fourier shell correlation (FSC) curves.

Main Results:

  • The inverse cubic resolution scale transformation results in resolution shells with approximately equal numbers of Fourier coefficients.
  • This approach effectively emphasizes the high-resolution region, crucial for detailed structural analysis.
  • Fourier shell correlation (FSC) curves transformed into profiles amenable to piecewise linear interpolation, suggesting enhanced robustness.

Conclusions:

  • Defining resolution shells using the inverse cubic scale offers a more balanced and potentially less biased approach for analyzing periodic functions in cryo-electron microscopy (cryoEM).
  • This method can improve the reliability of statistical comparisons and the interpretation of Fourier shell correlation (FSC) analyses.